Abstract: In this paper, we discuss the application of Quantum Approximation Optimization Algorithm (QAOA) in portfolio optimization problems, which, under discrete constraints, is proved to be NP-hard. We introduce the fundamental framework of QAOA and the corresponding modeling of portfolio optimization problems. We illustrate several variants of QAOA applicable to portfolio optimization problems. Next, we examine their performances and the performance of the classical method with numerical simulation and hypothesis testing. The average approximation ratio of each quantum algorithm is at least 7% higher than that of the classical algorithm.